The bottom line is really quite simple...
1) if the Local Sidereal Time (LST) are the same on the ASIAIR and on the mount, then everything should be in sync.
Punkt. That's it.
The reason is that the Hour Angle (HA) of the mount (the angle of the mechanical RA axis relative to the Meridian) and the RA of a star is related by
RA = LST - HA.
The problem is that unlike other programs, ASIAIR does not display its LST (even SkySafari shows LST).
2) So, we sanity check by using UTC and Local Longitude. If UTC on ASIAIR and mount agree, and Local Longitude of ASIAIR and mount agree, then you are also OK.
(UTC is related to Greenwich Sidereal Time by a known equation (related to Julian Date), and since we know the longitude difference, we also know the LST from just UTC and Local Longitude.)
The problem with the ASIAIR is that it does not understand Daylight Saving Time (DST) and ZWO also don't seem to understand that you don't even need to know the DST offset or UTC offset. You simply need to know the absolute UTC!
So, with every other programs, just check that LST of the program and the mount are in agreement.
With ASIAIR, check that UTC (not UTC offset) and the Local Longitude are in agreement.
ASIAIR also don't seem to understand the concept of East and West longitudes and often report a West Longitude as (360º - West Longitude). So, if it shows a longitude that is larger than 180º just subtract that number from 360º and flip the 'E' to 'W', or vice versa. If that corrected Longitude agrees with your Local Longitude, you are good to go.
Chen
P.S., If you are interested in navigation and celestial astronomy, I very highly recommend Dava Sobel's book: "Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time." She explained that when you are at sea, you need an accurate clock to determine Longitude relative to Greenwich. Today, we have GPS satellites to give us an accurate time relative to Greenwich :-).
